Mathematically modelling the spread of hepatitis C in injecting drug users

Corson, S and Greenhalgh, D and Hutchinson, S (2012) Mathematically modelling the spread of hepatitis C in injecting drug users. Mathematical Medicine and Biology, 29 (3). pp. 205-230. ISSN 1477-8599

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Abstract

Mathematical modelling can provide valuable insights into the biological and epidemiological properties of infectious diseases as well as the potential impact of intervention strategies employed by health organizations worldwide. In this paper, we develop a deterministic, compartmental mathematical model to approximate the spread of the hepatitis C virus (HCV) in an injecting drug user (IDU) population. Using analytical techniques, we find that the model behaviour is determined by the basic reproductive number R(0), where R(0) = 1 is a critical threshold separating two different outcomes. If R(0) ≤ 1 and HCV is initially present in the population, we find that the system will reach a disease-free equilibrium where HCV has been eliminated in all IDUs and needles. If R(0) > 1, then there is a unique positive endemic equilibrium which we show is locally stable. We then use simulations to verify our analytical results and examine the effect of different parameter values and intervention measures on HCV prevalence estimates.